Translation of abstract (English)

In this thesis we introduce a discontinuous Galerkin method for the numerical solution of hyperbolic conversation laws, as for example the compressible Euler equations of gas dynamics. Based on this finite element method, we develop an adaptive algorithm for the efficient computation of physically relevant quantities of the solution. This includes a posteriori error estimation of the error in the computed quantity as well as adaptive mesh design specifically tailored to the efficient computation of this quantity. We illustrate this approach by several different hyperbolic problems in combination with various different target quantities, including the efficient computation of drag and lift coefficients of airfoils immersed in inviscid compressible gas flows.